The invention relates generally to the field of mathematical modeling. More specifically, the invention relates to a method and system for developing a real-time gas turbine engine model.
Early real-time gas turbine engine models used piecewise linear state variable models (SVM) that described a reasonable behavior of an engine during steady state operation and mild transients. As processor speeds increased, more complex models that were a combination of linear and non-linear physics based elements were created. While the latter provided greater fidelity for transient operation and an engine's operational flight envelope, the accuracy required for long-term performance tracking as well as the need to address engine-to-engine variation needed improving.
Shown in FIG. 1 is an early on-board engine model system 101 used for performance tracking. The major components include the monitored engine 103, a physics-based engine model 105 and a performance estimation module 107. The physics-based engine model 105 is typically an SVM and the performance estimation module 107 is a Kalman filter observer.
The engine model 101 is driven by a set of input parameters 109 that command the engine 103. The input parameters comprise flight parameters such as Mach number, altitude, ambient conditions and others, and power setting parameters such as fuel flow, engine bleed air commands, variable geometry vane commands and others. The monitored engine output parameters 111 comprise gas path parameters such as internal shaft speeds, compressor, combustor and turbine temperatures and pressures and others. The physics-based engine model 105 outputs estimated parameters 113 corresponding to each engine 103 output parameter 111.
The estimated parameters 113 may be used for a variety of purposes. The parameters 113 provide for analytical redundancy if a channel mismatch were to occur, for example, in a multichannel redundant system such as a Full Authority Digital Engine Control (FADEC) (not shown), serving as an auctioneer between two redundant signals that have different values.
The physics-based engine model 105 estimated output parameters 113 are compared with the engine output parameters 111 to form residuals 115. If the physics-based engine model 105 is an accurate representation of the monitored engine 103, the residuals 115 should be close to zero on the average. However, as engine performance deteriorates over time, the residuals 115 deviate from zero.
The performance estimator 107 uses the residuals 115 to observe changes in performance across the engine's modules, in the form of adiabatic efficiencies, flow capacities, and turbine nozzle area deltas. This type of analysis is referred to as Gas Path Analysis (GPA) or Module Performance Analysis (MPA). The disparities between the physics-based engine model 105 and engine 103 outputs are used to modify the performance output of the engine model 105 estimated outputs 113 to drive the residuals 115 to zero (on the average). In this manner, the physics-based engine model 105 estimated outputs 113 more accurately reflect the current state of the engine 103 and the module performance deltas can be tracked over time to aid in determining proper engine work scope when the engine is removed for maintenance.
The model 101 described above represents an ideal situation where the physics-based engine model 105 is a faithful representation of the engine 103 being monitored. However, the physics-based engine model 105 does not hold true over time. Engine-to-engine variations, models simplified in order to run real-time and deviations caused by improvements to the engine's hardware, bleed and stator vane schedules, cooling flows, handling bleeds and others, over the engine's life cycle are not reflected in the model 105 and contribute to output disparities between the physics-based engine model 105 and engine 103. The disparities result in inaccurate and misleading estimations in the module performance tracking for the system 101.
One approach taken to obviate engine model deviations over time is a hybrid engine model. The hybrid model incorporates both physics-based and empirical components. The hybrid architecture automatically modifies a derived engine model to a particular configuration as an engine's characteristics change over its service life and conforms the model to the engine to insure accurate performance tracking.
FIGS. 2 and 3 show hybrid gas turbine engine modeling configurations. The hybrid system 201 shown in FIG. 2 derives an empirical model (EM) 203. The EM 203 represents the differences, or residuals 115, between measured engine output parameters 111 and the physics-based model output parameters 113. The engine 103, the physics-based engine model 105 and the EM 203 are driven by the same input parameters 109. The input parameters 109 may vary depending on engine type and application.
Once the EM 203 is derived, a hybrid engine model 301 may be implemented as shown in FIG. 3. An engine performance estimation 107 is used to track engine performance deviations for engine health diagnostic and prognostic purposes. This typically takes the form of a gas path analysis that estimates performance changes in the major modules of the engine on the basis of residual changes in parameters observed in the engine's gas path, such as temperatures, pressures, speeds, and others.
The performance changes are usually given in terms of thermodynamic parameters, such as changes in adiabatic efficiency and flow capacity for the compression modules, and changes in adiabatic efficiency and nozzle area for the turbine modules. Since the residual gas path data is used in this determination, the reference (from which the changes are estimated) is the engine model under consideration.
The EM 203 may use relationship models such as regression, autoregressive moving average (ARMA), artificial neural network (ANN), and others for prediction. The hybrid model 301 includes a physics-based engine model 105 and an EM 203 that models the difference between the physics-based engine model 105 and the engine 103 being monitored. The addition 305 of the physics-based engine model 105 and EM 203 outputs produces a hybrid model 303 representation of the monitored engine 103 as it appeared during the period of operation when residual data was gathered and processed to form the empirical element. A Kalman filter observer 107 is provided to perform the gas path analysis to monitor the engine's health 307 after the empirical model 203 is available.
To be effective, the system identification methods shown in FIGS. 2 and 3 should be performed on board in real-time during engine operation and flight to negate the need for establishing a data infrastructure to capture, store and transfer the requisite data for modeling to a ground computer for developing the empirical model element. Otherwise, the system 301 shown in FIG. 3 would require the storage and retention of engine and flight input data over a series of flights until a sufficient amount of flight and engine regime data was accumulated to complete the EM 203. This would impose an unrealistic storage capacity requirement for the system.
To reduce the size of the modeling problem as well as the amount of flight data storage required to fit the model, one methodology incrementally builds an EM using a flight envelope partition to create smaller EM sub-models. An example of a flight envelope partition is shown in FIG. 4.
The flight envelope is given in terms of altitude and Mach number and defines the flight regime for which the engine under consideration is equipped to operate. The partition is simply a subdivision of this region into smaller regions referred to as cells 401. These regions are typically taken to be rectangular areas and are characterized by their height (altitude) and width (Mach) and a center coordinate 403. Data collected within a given cell is used to generate an empirical sub-model that represents the difference between the physics-based engine model estimated parameters and the actual engine's measured parameters in that region of the flight envelope. These empirical sub-models are incrementally assembled as flight data becomes available in a given cell.
The partitioning of the flight envelope contributes to the concept of sequential modeling in that it allows the construction of a series of sub-models to represent the model space. Since the flight envelope grid is predefined in order to limit the number of sub-models, it is likely that insufficient data within a given grid element would be collected during a single flight to properly model that subspace. No matter what particular modeling methodology is used, the entire set of data would have to be maintained for the proper modeling of the given sub-region. Extending this process across the entire partitioned flight envelope would require storing an enormous amount of data that would be impractical and prohibitive.
What is desired is a methodology for constructing the empirical model in an incremental manner without the requirement for storing all of the original data.